Solve for $x$ and $y$ using elimination. $\begin{align*}-2x-6y &= -2 \\ x-9y &= -6\end{align*}$
Answer: We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $1$ and the bottom equation by $2$ $\begin{align*}-2x-6y &= -2\\ 2x-18y &= -12\end{align*}$ Add the top and bottom equations. $-24y = -14$ Divide both sides by $-24$ and reduce as necessary. $y = \dfrac{7}{12}$ Substitute $\dfrac{7}{12}$ for $y$ in the top equation. $-2x-6( \dfrac{7}{12}) = -2$ $-2x-\dfrac{7}{2} = -2$ $-2x = \dfrac{3}{2}$ $x = -\dfrac{3}{4}$ The solution is $\enspace x = -\dfrac{3}{4}, \enspace y = \dfrac{7}{12}$.